Detection of Anticipatory Dynamics Between a Pair of Zebrafish

TL;DR

This study investigates anticipatory dynamics in zebrafish pairs by analyzing trajectories and using transfer entropy to determine causal flow, revealing gender differences and internal dynamics in interactions.

Contribution

It introduces a method to detect anticipatory dynamics in natural systems using transfer entropy and applies it to zebrafish, supported by simulations of chaotic oscillators.

Findings

Anticipatory dynamics are more common in mixed-gender zebrafish pairs.

Transfer entropy effectively determines causal order in fish interactions.

Fish interactions are driven by internal dynamics, not adaptation.

Abstract

Trajectories from a pair of interacting zebrafish are used to test for the existence of anticipatory dynamics in natural systems. Anticipatory dynamics (AD) is unusual in that causal events are not necessarily ordered by their temporal order. However, their causal order can still be established if the direction of information flow (DIF) is known. In order to obtain DIF between trajectories of the two fish, we have made use of the difference of the transfer entropy between the trajectories with a history length established by experiments with known DIF. Our experimental results indicate that AD can be observed much more often in fish pairs of different genders. The use of DIF to determine causal order is further verified by the simulation of two chaotic Lorenz oscillators with anticipatory coupling; mimicking the interaction between the fish. Our simulation results further suggest that the two fish are interacting with their own internal dynamics, not by adaptation.